# Introductory Discrete Mathematics

## V. K. Balakrishnan

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This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. Geared toward mathematics and computer science majors, it emphasizes applications, offering more than 200 exercises to help students test their grasp of the material and providing answers to selected exercises. 1991 edition.

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Contenuti:

Preface 0 Set Theory and Logic 0.1 Introduction to Set Theory 0.2 Functions and Relations 0.3 Inductive Proofs and Recursive Definitions 0.4 The Language of Logic 0.5 Notes and References 0.6 Exercises 1 Combinatorics 1.1 Two Basic Counting Rules 1.2 Permutations 1.3 Combinations 1.4 More on Permutations and Combinations 1.5 The Pigeonhole Principle 1.6 The Inclusion-Exclusion Principle 1.7 Summary of Results in Combinatorics 1.8 Notes and References 1.9 Exercises 2 Generating Functions 2.1 Introduction 2.2 Ordinary Generating Functions 2.3 Exponential Generating Functions 2.4 Notes and References 2.5 Exercises 3 Recurrence Relations 3.1 Introduction 3.2 Homogeneous Recurrence Relations 3.3 Inhomogeneous Recurrence Relations 3.4 Recurrence Relations and Generating Functions 3.5 Analysis of Alogorithms 3.6 Notes and References 3.7 Exercises 4 Graphs and Digraphs 4.1 Introduction 4.2 Adjacency Matrices and Incidence Matrices 4.3 Joining in Graphs 4.4 Reaching in Digraphs 4.5 Testing Connectedness 4.6 Strong Orientation of Graphs 4.7 Notes and References 4.8 Exercises 5 More on Graphs and Digraphs 5.1 Eulerian Paths and Eulerian Circuits 5.2 Coding and de Bruijn Digraphs 5.3 Hamiltonian Paths and Hamiltonian Cycles 5.4 Applications of Hamiltonian Cycles 5.5 Vertex Coloring and Planarity of Graphs 5.6 Notes and References 5.7 Exercises 6 Trees and Their Applications 6.1 Definitions and Properties 6.2 Spanning Trees 6.3 Binary Trees 6.4 Notes and References 6.5 Exercises 7 Spanning Tree Problems 7.1 More on Spanning Trees 7.2 Kruskal's Greedy Algorithm 7.3 Prim's Greedy Algorithm 7.4 Comparison of the Two Algorithms 7.5 Notes and References 7.6 Exercises 8 Shortest Path Problems 8.1 Introduction 8.2 Dijkstra's Algorithm 8.3 Floyd-Warshall Algorithm 8.4 Comparison of the Two Algorithms 8.5 Notes and References 8.6 Exercises Appendix What is NP-Completeness? A.1 Problems and Their Instances A.2 The Size of an Instance A.3 Algorithm to Solve a Problem A.4 Complexity of an Algorithm A.5 "The "Big Oh" or the O(·) Notation" A.6 Easy Problems and Difficult Problems A.7 The Class P and the Class NP A.8 Polynomial Transformations and NP-Completeness A.9 Coping with Hard Problems Bibliography Answers to Selected Exercises Index

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Book by Balakrishnan V K

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## 1.Introductory Discrete Mathematics Format: Trade Paper

Editore: Dover Publishers
ISBN 10: 0486691152 ISBN 13: 9780486691152
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Descrizione libro Dover Publishers. Condizione libro: New. Brand New. Codice libro della libreria 0486691152

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## 2.Introductory Discrete Mathematics

Editore: Dover Publications Inc. (1996)
ISBN 10: 0486691152 ISBN 13: 9780486691152
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Descrizione libro Dover Publications Inc., 1996. PAP. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days. Established seller since 2000. Codice libro della libreria IB-9780486691152

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## 3.Introductory Discrete Mathematics (Paperback)

Editore: Dover Publications Inc., United States (2010)
ISBN 10: 0486691152 ISBN 13: 9780486691152
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Descrizione libro Dover Publications Inc., United States, 2010. Paperback. Condizione libro: New. New edition. 231 x 170 mm. Language: English . Brand New Book. This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems. Chapters 0-3 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material. Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization ? the minimal spanning tree problem and the shortest distance problem ? are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix. Codice libro della libreria AAC9780486691152

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## 4.Introductory Discrete Mathematics (Paperback)

Editore: Dover Publications Inc., United States (2010)
ISBN 10: 0486691152 ISBN 13: 9780486691152
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Descrizione libro Dover Publications Inc., United States, 2010. Paperback. Condizione libro: New. New edition. 231 x 170 mm. Language: English . Brand New Book. This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems. Chapters 0-3 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material. Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization ? the minimal spanning tree problem and the shortest distance problem ? are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix. Codice libro della libreria AAC9780486691152

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## 5.Introductory Discrete Mathematics (Dover Books on Computer Science)

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## 6.Introductory Discrete Mathematics (Dover Books on Computer Science)

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Descrizione libro Dover Publications. PAPERBACK. Condizione libro: New. 0486691152 Brand New Book. Ships from the United States. 30 Day Satisfaction Guarantee!. Codice libro della libreria 14270177

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## 7.Introductory Discrete Mathematics

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Descrizione libro Dover Publications. Paperback. Condizione libro: New. Paperback. 256 pages. Dimensions: 9.1in. x 6.7in. x 0.5in.This concise text offers an introduction to discrete mathematics for undergraduate students in computer science and mathematics. Mathematics educators consider it vital that their students be exposed to a course in discrete methods that introduces them to combinatorial mathematics and to algebraic and logical structures focusing on the interplay between computer science and mathematics. The present volume emphasizes combinatorics, graph theory with applications to some stand network optimization problems, and algorithms to solve these problems. Chapters 03 cover fundamental operations involving sets and the principle of mathematical induction, and standard combinatorial topics: basic counting principles, permutations, combinations, the inclusion-exclusion principle, generating functions, recurrence relations, and an introduction to the analysis of algorithms. Applications are emphasized wherever possible and more than 200 exercises at the ends of these chapters help students test their grasp of the material. Chapters 4 and 5 survey graphs and digraphs, including their connectedness properties, applications of graph coloring, and more, with stress on applications to coding and other related problems. Two important problems in network optimization the minimal spanning tree problem and the shortest distance problem are covered in the last two chapters. A very brief nontechnical exposition of the theory of computational complexity and NP-completeness is outlined in the appendix. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Codice libro della libreria 9780486691152

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## 8.Introductory Discrete Mathematics (Paperback)

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Descrizione libro Paperback. Condizione libro: New. 13mm x 19mm x 231mm. Paperback. This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. Geared toward mathematics an.Shipping may be from multiple locations in the US or from the UK, depending on stock availability. 256 pages. 0.318. Codice libro della libreria 9780486691152

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## 9.Introductory Discrete Mathematics (Dover Books on Mathematics)

Editore: Dover Publications Inc. 1996-11-22 (1996)
ISBN 10: 0486691152 ISBN 13: 9780486691152
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Descrizione libro Dover Publications Inc. 1996-11-22, 1996. Condizione libro: New. Brand new book, sourced directly from publisher. Dispatched within 2 working days from our warehouse. Book will be sent in robust, secure packaging to ensure it reaches you securely. Codice libro della libreria NU-ING-00310368

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## 10.Introductory Discrete Mathematics (New edition)

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Descrizione libro Dover Publications Inc. Paperback. Condizione libro: new. BRAND NEW, Introductory Discrete Mathematics (New edition), V.K. Balakrishnan. Codice libro della libreria B9780486691152

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